Analysis and Design of an UWB Band pass Filter with Improved Upper Stop band Performanes Nadia Benabdallah, 1 Nasreddine Benahmed, 2 Fethi Tari Bendimerad 3 1 Department of Physis, Preparatory Shool of Sienes and Tehnology (EPST-Tlemen), Tlemen, Algeria 23 Department of Teleommuniations, University of Tlemen, Algeria Abstrat: In this wor, we are interesting in the analysis and the design of an ultra wideband (UWB) band pass filter with improved upper stop band performanes, using mirostrip lines. The design of the UWB band pass filter is based on the use of stepped-impedane low pass filter and high pass filter; whereas the simulation of its frequeny response ([S]) is done using MATPAR software and it is based on the eletromagneti (EM) parameters for eah setion of line forming the band pass struture. Our filter with bandwidth between 2.9-10.8 GHz, measures just 12.6 1.524 31.58 mm and was fabriated using RT/D 5880 substrate by means of stepped-impedane 5-pole mirostrip low pass filter and high pass filter onstruted from quasilumped elements. The simulated results of stop band performanes are better than 15 db for a frequeny range up to 25 GHz. Keywords: Analysis design and simulation, EM-parameters, UWB band pass filter, stepped-impedane low pass filter, high pass filter with quasilumped elements, MATPAR software, S-parameters. I. INTRODUCTION FILTERS play important roles in many RF/mirowave appliations. They are used to separate or ombine different frequenies. The eletromagneti (EM) spetrum is limited and has to be shared; filters are used to selet or onfine the RF/mirowave signals within assigned spetral limits. Emerging appliations suh as wireless ommuniations ontinue to hallenge RF/mirowave filters with ever more stringent requirements-higher performane, smaller size, lighter weight, and lower ost. Depending on the requirements and speifiations, RF/mirowave filters may be designed as lumped element or distributed element iruits; they may be realized in various transmission line strutures, suh as waveguide, oaxial line [1-2], and mirostrip [3-4]. The reent advane of novel materials and fabriation tehnologies, inluding monolithi mirowave integrated iruit (MMIC), miroeletromehani system (MEMS), miromahining, high-temperature superondutor (HTS), and low-temperature ofired eramis (LTCC), has stimulated the rapid development of new mirostrip and other filters [5]. In the meantime, advanes in omputer-aided-engineering (CAE) tools suh as full-wave eletromagneti (EM) simulators have revolutionized filter design. Many novel mirostrip filters with advaned filtering harateristis have been demonstrated [5]. With the ready availability of aurate CAE tools, it is possible to apply some basi formulas for alulating the dimensions of these filters and simulating their frequeny responses [5]. In this wor, we are interesting in the analysis and the design of an ultra wideband (UWB) band pass filter with improved upper stop band performanes, using mirostrip lines. The design of the UWB band pass filter is based on the use of stepped-impedane low pass filter and high pass filter onstruted from quasilumped elements. The utoff frequenies of 3.1 and 10.6 GHz were seleted respetively for eah type of filter. Our filter has not only ompat size but also a wider upper stop band resulting from low pass harateristis. The simulated results of stop band performanes are better than 15 db for a frequeny range up to 25 GHz. What follows are the analysis, the design and the simulation of this UWB band pass filter. II. BASIC CONCEPTS This setion desribes the basi onepts and theories neessary for the overall design of RF/mirowave filters inluding mirostrip lines strutures. The transfer funtion of a two-port filter networ is a mathematial desription of networ response harateristis, namely, a mathematial expression of S 21. On many oasions, an amplitude-squared transfer funtion for a lossless passive filter networ is defined as: 2 1 S 21( j) 2 2 (1) 1 ( ) F n Where ε is a ripple onstant, F n (ω) represents a filtering or harateristi funtion, and ω is a frequeny variable. For our disussion here, it is onvenient to let ω represent a radian frequeny variable of a low pass prototype filter that has a utoff frequeny at ω = ω (rad/s). 1105 Page
For a given transfer funtion of equation (1), the insertion loss response of the filter an be omputed by: L A 1 ( ) 10 log 2 S ( j) 21 ( db) (2) Sine S 11 2 + S 21 2 =1 for a lossless, passive two-port networ, the return loss response of the filter an be expressed by: L R 2 1 S21 ( j) ( db) ( ) 10 log (3) The transfer funtion is an essential feature of the filter. It is given by different mathematial laws alled filtering funtion. The most ones used are: Butterworth and Chebyshev laws. II.1 Butterworth (Maximally Flat) response The amplitude-squared transfer funtion for Butterworth filters that have an insertion loss L Ar =3.01 db at the utoff frequeny ω is given by: 2 1 (4) S 21 ( j ) 2. n 1 Where n is the degree or the order of filter, whih orresponds to the number of reative elements, required in the low pass prototype filter. This type of response is also referred to as maximally flat beause its amplitude-squared transfer funtion defined in equation (4) has the maximum number of (2n-1) zero derivatives at ω=0. Figure 1 shows a typial maximally flat response. Fig. 1. Butterworth (maximally flat) low pass response. II.2 Chebyshev response The Chebyshev response that exhibits the equal-ripple pass band and maximally flat stop band is depited in figure 2. The amplitude-squared transfer funtion that desribes this type of response is: 2 1 S ( j) (5) 21 2 2 1 T n ( ) Where: The ripple onstant ε is related to a given pass band ripple L Ar in db by: L Ar 10 10 1 (6) T n (ω) is a Chebyshev funtion of the first ind of order n, whih is defined as 1 os n os T n( ) 1 osh n osh for for 1 1 (7) Fig. 2. Chebyshev low pass response. 1106 Page
II.3 Low pass prototype filter and elements The main objetive of this setion is to present equations for obtaining element values of some ommonly used low pass prototype filters. In addition, the determination of the degree of the prototype filter will be disussed. In general, the design of mirostrip low pass filters involves two main steps. The first one is to selet an appropriate low pass prototype (figure 3). The hoie of the type of response, inluding pass band ripple and the number of reative elements, will depend on the required speifiations. The ouples [L A ; (ω/ω )] that we want to obtain at ω=ω a allows us to find the values of the order n of the filter while the L and C values are determined using the following g parameters. Fig. 3. Low pass prototype filter For Butterworth or maximally flat low pass prototype filters having a transfer funtion given in (4), the g parameters may be omputed using: g 0 1 2 1 g 2sin 2n 1 to n (8) g n1 1 For Chebyshev low pass prototype filters having a transfer funtion given in (5), the element values for the two-port networs may be omputed using the following g parameters: g 0 1 2 g1 sin 2n 2 1 2 3 4 sin sin 1 2n 2n (9) g 2,..., n g 2 2 1 1 sin n 10. forn odd g n 1 2 oth forn even 4 Where: sinh 2n L ln oth Ar 17.37 The input resistane R e is given by the terms of referene sine it is the harateristi impedane of the line on whih the filter is inserted. Generally it is 50Ω. The load resistane an be alulated by: R r. (10) s R e Where: for Butterworth r = 1 and for Chebyshev response 10. fornodd LAr r oth 2 with r In r tgh forneven 17.37 4 Finally the values of the elements L and C of low pass filter are omputed using relations (11) and (12): Re L g (11) C e 1 1 g (12) R II.4 High pass filter and elements The following figure shows the struture of a high pass filter transformed from the low pass prototype and using L- C elements. 1107 Page
Fig. 4. High pass filter This simple form of high pass filter onsists of a series apaitor, whih is often found in appliations for diret urrent or d blo. For more seletive high pass filters, more elements are required. This type of high pass filter an be easily designed based on a lumped-element low pass prototype suh as one shown in figure 4 and on the following relations: Re L (13) g C e 1 (14) R g II.5 Band pass filter and elements Figure 5 shows the struture of a band pass filter using L-C elements. Fig. 5. Band pass filter The Chebyshev response of this type of filter is represented in figure 6. The resonane frequeny of the filter is indiated by ω 0 while the low and high pass frequenies are respetively ω 1 and ω 2. Fig. 6. Chebyshev band pass response. This type of band pass filter an be easily designed based on a lumped-element low pass prototype and on the following expressions: For the elements in series: L Re g B 0 (15) B C Re g 0 (16) For the elements in parallel: ReB L g 0 (17) g C ReB 0 (18) 2 1 Where: B 0 1108 Page
III. STEPPED-IMPEDANCE, L-C TYPE MICRO STRIP FILTERS Having obtained a suitable lumped-element filter design, the next main step in the design of mirostrip filters is to find an appropriate mirostrip realization that approximates the lumped element filter. In this setion, we onentrate on the seond step. Figure 7 shows a general struture of the stepped-impedane low pass mirostrip filters, whih uses a asaded struture of alternating high- and low impedane transmission lines. The high-impedane lines at as series indutors and the low-impedane lines at as shunt apaitors. Therefore, this filter struture is diretly realizing the L-C ladder type of low pass filters of figure 3. Fig. 7. General struture of the stepped-impedane low pass mirostrip filters. Figures 8 to 10 present three mirostrip realizations of low pass, high pass and band pass filters. a) b) Fig. 8. Layout of a 3-pole mirostrip low pass filter realized on a substrate with a relative dieletri onstant of 10.8 and a thiness of 1.27 mm and using: stepped-impedane on a) and open-iruited stubs on b) [5]. Fig. 9. A mirostrip optimum high pass filter on a substrate with a relative dieletri onstant of 2.2 and a thiness of 1.57 mm [5] Fig. 10. Layout of a designed mirostrip band pass filter with half-wavelength open-iruited stubs on a 0.635 mm thi substrate with a relative dieletri onstant of 10.2 [5]. These strutures have been studied and analyzed by various ommerial EM simulation softwares. Their frequeny responses are in good agreement with the requirements and speifiations. 1109 Page
IV. EM ANALYSES AND DESIGN Using the theory presented in this paper, we realized an aurate CAE tool whih allows obtaining a suitable lumped-element filter design and finding an appropriate mirostrip realization that approximates the lumped element filter. The frequeny responses of our filters designs fabriated with mirostrip lines an be obtained using MATPAR [6] or other software. Our CAE tool suitable for low pass, high pass and band pass RF/mirowave filters ahieves a qui design aording to Butterworth or Chebyshev responses and gives same results as those obtained with ommerial eletromagneti (EM) simulation software. Here we applied it to the analysis and the design of an UWB band pass filter with improved upper stop band performanes. The design of the UWB band pass filter is based on the use of stepped-impedane low pass filter and high pass filter onstruted from quasilumped elements. An example of design of a three-pole low pass filter is illustrated in figure 11. The speifiations for the filter under onsideration are: utoff frequeny f of 1 GHz, pass band ripple of 0.1 db (or return loss < 16.42 db) and soure impedane of 50 Ω. On a substrate with a relative dieletri onstant of 10.8 and a thiness of 1.27 mm, figures 11-b and 11- give two types of realizations that approximate the lumped element filter of figure 11-a. The first one uses stepped-impedane and the seond one uses open-iruited stubs. Our obtained results are in good agreement with those shown in figure 8. a) b) ) Fig. 11. Lumped-element filter design on a) and layouts: stepped impedane on b) and open-iruited on ) (Unit: mm). High pass filters onstruted from quasilumped elements may be desirable for many appliations, provided that these elements an ahieve good approximation of desired lumped elements over the entire operating frequeny band. As part of this study on UWB mirostrip lines band pass filters, we examined first the design of a high pass mirostrip filter having a utoff frequeny f of 3.1 GHz, pass band ripple of 0.1 db and soure impedane of 50 Ω. Using design proedure we find the lumped elements of the following iruit. Fig. 12. Lumped-element highpass filter design. A possible realization of suh a high pass filter in mirostrip, using quasilumped elements, is shown in figure 13. Here it is seen that the series apaitors are realized by two idential interdigital apaitors, and the shunt indutor is realized by a short-iruited stub. The mirostrip high pass filter is designed on a ommerial substrate (RT/D 5880) with a relative dieletri onstant of 2.2 and a thiness of 1.524 mm. 1110 Page
S 21 (db) International Journal of Modern Engineering Researh (IJMER) Fig. 13. A quasilumped highpass filter in mirostrip on a substrate with a relative dieletri onstant of 2.2 and a thiness of 1.524 mm (Unit: mm). In order to failitate the analysis of suh struture under MATPAR environment, we divided it to three setions of lines (Figure 13). The obtained EM parameters of eah setion of lines using LINPAR software [7] are: - For the interdigital apaitors (setions 1 and 3): 772.0 41.38 28.57 21.24 16.43 13.10 41.38 763.3 40.97 28.34 21.12 16.43 28.57 40.97 761.4 40.89 28.34 21.24 nh L 21.24 28.34 40.89 761.4 40.97 28.57 m 16.43 21,12 28.34 40.97 763.3 41.38 13,10 16.43 21.24 28.57 41.38 771.9 32.460 14.47 2.68 1.06 0.54 0.44 14.47 39.20 13.28 2.23 0.85 0.54 2.68 13.28 39.40 13.21 2.23 1.06 pf C 1.06 2.23 13.21 39.40 13.21 2.68 m 0.54 0.85 2.23 13.28 39.20 14.47 0.44 0.54 1.06 2.68 14.47 32.46 - For the shunt indutor (setion 2): L = 218.0 nh/m; C = 96.8 pf/m; Z = 47.52 Ω and ε eff = 1.4. We applied the MATPAR software in the aim of heing the eletrial performane of the designed high pass filter shown in figure 13. Figure 14 illustrates the simulated response (S 21 ) of the high pass filter onstruted from quasilumped elements, in the frequeny band [0.2-25] GHz. It an be seen that for S 21 =-3 db the utoff frequeny is 2.9 GHz. 10 0-10 -20-30 -40-50 -60-70 -80-90 -100-110 0,00E+000 5,00E+009 1,00E+010 1,50E+010 2,00E+010 2,50E+010 Frequeny (Hz) Fig. 14. EM simulated performane of the quasilumped high pass filter. For the seond part of our study on UWB mirostrip lines band pass filters, we examined the design of a low pass mirostrip filter having a utoff frequeny f of 10.6 GHz, pass band ripple of 0.1 db and soure impedane of 50 Ω. Using design proedure we find the lumped elements of the iruit shown in figure 15. 1111 Page
S 21 (db) International Journal of Modern Engineering Researh (IJMER) Fig. 15. Lumped-element low pass filter design. A layout of this designed mirostrip filter is illustrated in figure 16, and its performane obtained by MATPAR software is plotted in figure 17. Fig. 16. Layout of the designed stepped-impedane low pass filter realized on a substrate with a relative dieletri onstant of 2.2 and a thiness of 1.524 mm (Unit: mm). 0-2 -4-6 -8-10 -12 0,00E+000 5,00E+009 1,00E+010 1,50E+010 2,00E+010 2,50E+010 Frequeny (Hz) Fig. 17. EM simulated performane of the designed stepped-impedane low pass filter. The frequeny response of the stepped-impedane low pass filter was obtained for the EM parameters listed into table1 of eah setion of line forming the designed struture. From this response it an be seen that the utoff frequeny of the filter is 10.53 GHz obtained for S 21 =-3 db. Table I. EM parameters of eah setion of line of the stepped-impedane low pass filter Setion [L] [C] Z (Ω) of line (nh/m) (pf/m) Ω e ff 1 412.4 47.95 92.8 1.78 2 113.7 196.6 24.0 2.0 3 412.4 47.95 92.8 1.78 Finally the layout of the designed UWB band pass filter using a 3-pole mirostrip low pass filter is illustrated in figure 18, and its performane obtained by MATPAR software is plotted in figure 19 in the frequeny band [0.2-25] GHz. This response is in reasonable agreement with results of planar strutures and it also meets the requirements for UWB appliations per the FCC [8]. The simulated results of stop band performanes are better than 5 db for a frequeny range up to 25 GHz. 1112 Page
S 21 (db) S 21 (db) International Journal of Modern Engineering Researh (IJMER) In order to inrease the stop band performanes of our designed struture, figure 20 gives the layout of the final UWB band pass filter using a 5-pole mirostrip low pass filter. In figure 21 we present the frequeny response of our designed filter. Fig. 18. Layout of the designed UWB band pass struture using a 3-pole miro strip low pass filter 0-5 -10-15 -20-25 -30-35 -40-45 -50-55 -60-65 0,00E+000 5,00E+009 1,00E+010 1,50E+010 2,00E+010 2,50E+010 Frequeny (Hz) Fig. 19. EM simulated performane of the designed UWB band pass struture using a 3-pole miro strip low pass filter. Fig. 20. Layout of the designed UWB band pass struture using a 5-pole mirostrip low pass filter 0-5 -10-15 -20-25 -30-35 -40-45 -50-55 -60-65 -70-75 0,00E+000 5,00E+009 1,00E+010 1,50E+010 2,00E+010 2,50E+010 Frequeny (Hz) Fig. 21. EM simulated performane of the designed UWB band pass struture using a 5-pole miro strip low pass filter. Our filter, whih measures just 12.6 1.524 31.58 mm, was fabriated using RT/D 5880 substrate by means of stepped-impedane 5-pole mirostrip low pass filter and high pass filter onstruted from quasilumped elements. The simulated results of stop band performanes are better than 15 db for a frequeny range up to 25 GHz. 1113 Page
V. CONCLUSION In summary, this wor presented the analysis, the design and the simulation of an ultra wideband band pass filter with improved upper stop band performanes, using miro strip lines. The filter whih measures just 12.6 1.524 31.58 mm, was fabriated using RT/D 5880 substrate by means of stepped-impedane 5-pole miro strip low pass filter and high pass filter onstruted from quasilumped elements. The simulated results of stop band performanes are better than 15 db for a frequeny range up to 25 GHz. It was designed using our aurate CAE tools and with the aid of MATPAR software, although other ommerial EM simulation software an also be used. REFERENCES [1] A. Benaddour, N. Benahmed, N. Benabdallah and F.T. Bendimerad, Create UWB filters with oaxial ables, Mirowaves & RF, 51(7), July 2012, 59-63. [2] N. Benahmed, N. Benabdallah, S. Seghier, F.T. Bendimerad and B. Benyouef, Analyzing an UWB band pass filter for high power appliations using retangular oaxial ables with square inner ondutors, Ciruits and Systems (CS), 2(3), July 2011, 121-126. [3] N. Benahmed, N. Benabdallah, F.T. Bendimerad and B. Benyouef, Analyse et oneption d un filtre stop-bande multiouhe miro-usiné à oupleur miro ruban asymétrique, Lebanese Siene Journal (LSJ), 12(1), 2011, 45-58. [4] N. Benabdallah, N. Benahmed and F.T. Bendimerad, FEM Analysis, Design and Optimization of a Compat Bandpass Filter for Low-power UWB Communiations Appliations, International Journal of Mirowaves Appliations, 2(1), January-February 2013, 18-22. [5] J. S. Hong and M. J. Lanaster, Mirostrip Filters for RF/Mirowave Appliations (John Wiley & Sons, In., 2011). [6] A.R. Djordjevi, M. Bazdar, G. Vitosevi, T. Sarar, and R. F. Harrington, Sattering parameters of mirowave networs with multiondutor transmission lines (Arteh House, Norwood, MA, 1990). [7] A.R. Djordjevi, M.B. Bazdar, T.K. Saran, LINPAR for windows: Matrix parameters of multiondutor transmission lines, Software and user s manual (Arteh Housse, 1999). [8] FCC, Revision of Part 15 of the Commission's Rules Regarding Ultra-Wideband Transmission System, Tehnial Report ET-Doet 98-153, 14 February 2002. 1114 Page